df <- as_tibble(read.table("winequality-red.csv", sep=";", header = TRUE))
df_white <- as_tibble(read.table("winequality-white.csv", sep=";", header = TRUE))
index = sample(1:nrow(df), 0.7*nrow(df))
train = df[index,] # Create the training data
test = df[-index,] # Create the test data
dim(train)
## [1] 1119 12
dim(test)
## [1] 480 12
lm_basic <- lm(data = df, quality ~ .)
summary(lm_basic)
##
## Call:
## lm(formula = quality ~ ., data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.68911 -0.36652 -0.04699 0.45202 2.02498
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.197e+01 2.119e+01 1.036 0.3002
## fixed.acidity 2.499e-02 2.595e-02 0.963 0.3357
## volatile.acidity -1.084e+00 1.211e-01 -8.948 < 2e-16 ***
## citric.acid -1.826e-01 1.472e-01 -1.240 0.2150
## residual.sugar 1.633e-02 1.500e-02 1.089 0.2765
## chlorides -1.874e+00 4.193e-01 -4.470 8.37e-06 ***
## free.sulfur.dioxide 4.361e-03 2.171e-03 2.009 0.0447 *
## total.sulfur.dioxide -3.265e-03 7.287e-04 -4.480 8.00e-06 ***
## density -1.788e+01 2.163e+01 -0.827 0.4086
## pH -4.137e-01 1.916e-01 -2.159 0.0310 *
## sulphates 9.163e-01 1.143e-01 8.014 2.13e-15 ***
## alcohol 2.762e-01 2.648e-02 10.429 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.648 on 1587 degrees of freedom
## Multiple R-squared: 0.3606, Adjusted R-squared: 0.3561
## F-statistic: 81.35 on 11 and 1587 DF, p-value: < 2.2e-16
Volatile acidity, chlorides, total sulfur dioxide, sulphates and alcohol are all very statistically significant, although our adjusted \(R^2\) is still quite low.
train_control <- trainControl(method = "cv", number = 5)
model_ridge <- train(quality ~ .,
data = df,
method = "ridge", # method
trControl = train_control) # cross validation
model_ridge
## Ridge Regression
##
## 1599 samples
## 11 predictor
##
## No pre-processing
## Resampling: Cross-Validated (5 fold)
## Summary of sample sizes: 1280, 1279, 1280, 1278, 1279
## Resampling results across tuning parameters:
##
## lambda RMSE Rsquared MAE
## 0e+00 0.6528704 0.3479670 0.5060664
## 1e-04 0.6528690 0.3479702 0.5060643
## 1e-01 0.6526458 0.3490339 0.5051653
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was lambda = 0.1.
#something doesn't seem to be working here
model_stepwise <- train(quality ~ .,
data = df,
method = "glmStepAIC",
trControl = train_control)
## Start: AIC=2523.52
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 527.40 2521.6
## - fixed.acidity 1 527.41 2521.6
## - density 1 527.71 2522.3
## - residual.sugar 1 528.09 2523.2
## <none> 527.38 2523.5
## - free.sulfur.dioxide 1 528.34 2523.8
## - pH 1 528.68 2524.7
## - total.sulfur.dioxide 1 533.58 2536.5
## - chlorides 1 536.07 2542.4
## - volatile.acidity 1 549.06 2573.1
## - sulphates 1 552.36 2580.8
## - alcohol 1 560.98 2600.6
##
## Step: AIC=2521.55
## .outcome ~ fixed.acidity + volatile.acidity + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 527.42 2519.6
## - density 1 527.72 2520.3
## - residual.sugar 1 528.09 2521.2
## <none> 527.40 2521.6
## - free.sulfur.dioxide 1 528.42 2522.0
## - pH 1 528.69 2522.7
## - total.sulfur.dioxide 1 534.26 2536.1
## - chlorides 1 537.12 2542.9
## - sulphates 1 552.36 2578.8
## - volatile.acidity 1 557.41 2590.4
## - alcohol 1 561.23 2599.1
##
## Step: AIC=2519.6
## .outcome ~ volatile.acidity + residual.sugar + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 528.10 2519.3
## - residual.sugar 1 528.16 2519.4
## <none> 527.42 2519.6
## - free.sulfur.dioxide 1 528.46 2520.1
## - pH 1 531.56 2527.6
## - total.sulfur.dioxide 1 534.54 2534.8
## - chlorides 1 537.52 2541.9
## - sulphates 1 552.97 2578.2
## - volatile.acidity 1 558.59 2591.1
## - alcohol 1 589.06 2659.1
##
## Step: AIC=2519.27
## .outcome ~ volatile.acidity + residual.sugar + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 528.39 2518.0
## <none> 528.10 2519.3
## - free.sulfur.dioxide 1 529.27 2520.1
## - pH 1 531.73 2526.0
## - total.sulfur.dioxide 1 534.87 2533.6
## - chlorides 1 537.90 2540.8
## - sulphates 1 553.09 2576.4
## - volatile.acidity 1 559.48 2591.2
## - alcohol 1 626.08 2735.1
##
## Step: AIC=2517.97
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 528.39 2518.0
## - free.sulfur.dioxide 1 529.68 2519.1
## - pH 1 532.26 2525.3
## - total.sulfur.dioxide 1 534.93 2531.7
## - chlorides 1 537.98 2539.0
## - sulphates 1 553.18 2574.6
## - volatile.acidity 1 559.67 2589.6
## - alcohol 1 628.96 2739.0
## Start: AIC=2517.15
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - pH 1 525.13 2516.1
## <none> 524.76 2517.2
## - citric.acid 1 525.99 2518.1
## - free.sulfur.dioxide 1 526.19 2518.6
## - residual.sugar 1 526.21 2518.7
## - density 1 526.41 2519.2
## - fixed.acidity 1 527.15 2521.0
## - chlorides 1 531.07 2530.4
## - total.sulfur.dioxide 1 531.97 2532.6
## - sulphates 1 543.37 2559.7
## - volatile.acidity 1 550.54 2576.5
## - alcohol 1 555.68 2588.4
##
## Step: AIC=2516.05
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + sulphates + alcohol
##
## Df Deviance AIC
## <none> 525.13 2516.1
## - citric.acid 1 526.31 2516.9
## - free.sulfur.dioxide 1 526.41 2517.2
## - residual.sugar 1 527.35 2519.4
## - density 1 528.98 2523.4
## - chlorides 1 531.07 2528.4
## - total.sulfur.dioxide 1 532.00 2530.7
## - fixed.acidity 1 533.12 2533.4
## - sulphates 1 544.59 2560.6
## - volatile.acidity 1 551.06 2575.7
## - alcohol 1 562.76 2602.6
## Start: AIC=2585.23
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 554.30 2583.2
## - density 1 554.30 2583.2
## - residual.sugar 1 554.57 2583.9
## - citric.acid 1 555.12 2585.1
## <none> 554.30 2585.2
## - free.sulfur.dioxide 1 555.78 2586.6
## - pH 1 556.97 2589.4
## - total.sulfur.dioxide 1 561.07 2598.7
## - chlorides 1 562.66 2602.4
## - sulphates 1 574.27 2628.5
## - volatile.acidity 1 584.48 2651.0
## - alcohol 1 593.54 2670.7
##
## Step: AIC=2583.24
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 554.35 2581.3
## - residual.sugar 1 554.60 2581.9
## <none> 554.30 2583.2
## - citric.acid 1 555.17 2583.2
## - free.sulfur.dioxide 1 555.82 2584.7
## - pH 1 560.01 2594.3
## - total.sulfur.dioxide 1 561.57 2597.9
## - chlorides 1 563.24 2601.7
## - sulphates 1 574.60 2627.2
## - volatile.acidity 1 584.55 2649.1
## - alcohol 1 610.74 2705.2
##
## Step: AIC=2581.35
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 554.89 2580.6
## <none> 554.35 2581.3
## - citric.acid 1 555.24 2581.4
## - free.sulfur.dioxide 1 555.87 2582.9
## - pH 1 560.03 2592.4
## - total.sulfur.dioxide 1 562.03 2596.9
## - chlorides 1 563.63 2600.6
## - sulphates 1 575.96 2628.2
## - volatile.acidity 1 586.38 2651.1
## - alcohol 1 647.25 2777.4
##
## Step: AIC=2580.59
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 555.62 2580.3
## <none> 554.89 2580.6
## - free.sulfur.dioxide 1 556.66 2582.7
## - pH 1 560.64 2591.8
## - total.sulfur.dioxide 1 562.33 2595.6
## - chlorides 1 563.96 2599.3
## - sulphates 1 576.12 2626.6
## - volatile.acidity 1 586.45 2649.3
## - alcohol 1 649.49 2779.8
##
## Step: AIC=2580.28
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 555.62 2580.3
## - free.sulfur.dioxide 1 557.71 2583.1
## - pH 1 560.77 2590.1
## - total.sulfur.dioxide 1 563.87 2597.1
## - chlorides 1 565.72 2601.3
## - sulphates 1 576.45 2625.3
## - volatile.acidity 1 591.71 2658.7
## - alcohol 1 650.37 2779.5
## Start: AIC=2505.48
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 520.39 2503.5
## - density 1 520.42 2503.6
## - fixed.acidity 1 520.47 2503.7
## - citric.acid 1 520.88 2504.7
## <none> 520.38 2505.5
## - pH 1 522.42 2508.5
## - free.sulfur.dioxide 1 522.83 2509.5
## - chlorides 1 527.93 2521.9
## - total.sulfur.dioxide 1 529.52 2525.7
## - sulphates 1 543.79 2559.8
## - volatile.acidity 1 549.28 2572.6
## - alcohol 1 563.06 2604.3
##
## Step: AIC=2503.51
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + chlorides +
## free.sulfur.dioxide + total.sulfur.dioxide + density + pH +
## sulphates + alcohol
##
## Df Deviance AIC
## - density 1 520.43 2501.6
## - fixed.acidity 1 520.53 2501.8
## - citric.acid 1 520.90 2502.8
## <none> 520.39 2503.5
## - pH 1 522.57 2506.8
## - free.sulfur.dioxide 1 522.83 2507.5
## - chlorides 1 527.94 2519.9
## - total.sulfur.dioxide 1 529.56 2523.8
## - sulphates 1 545.02 2560.6
## - volatile.acidity 1 549.28 2570.6
## - alcohol 1 576.75 2633.0
##
## Step: AIC=2501.58
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + chlorides +
## free.sulfur.dioxide + total.sulfur.dioxide + pH + sulphates +
## alcohol
##
## Df Deviance AIC
## - citric.acid 1 520.92 2500.8
## - fixed.acidity 1 520.95 2500.9
## <none> 520.43 2501.6
## - free.sulfur.dioxide 1 522.85 2505.5
## - pH 1 522.93 2505.7
## - chlorides 1 527.94 2517.9
## - total.sulfur.dioxide 1 529.62 2522.0
## - sulphates 1 546.01 2561.0
## - volatile.acidity 1 549.50 2569.1
## - alcohol 1 615.26 2713.7
##
## Step: AIC=2500.8
## .outcome ~ fixed.acidity + volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 521.08 2499.2
## <none> 520.92 2500.8
## - pH 1 523.38 2504.8
## - free.sulfur.dioxide 1 523.76 2505.8
## - chlorides 1 530.27 2521.5
## - total.sulfur.dioxide 1 532.03 2525.8
## - sulphates 1 546.31 2559.7
## - volatile.acidity 1 555.84 2581.8
## - alcohol 1 617.53 2716.4
##
## Step: AIC=2499.19
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 521.08 2499.2
## - free.sulfur.dioxide 1 523.88 2504.0
## - pH 1 526.89 2511.4
## - chlorides 1 530.99 2521.3
## - total.sulfur.dioxide 1 532.72 2525.4
## - sulphates 1 546.96 2559.2
## - volatile.acidity 1 556.49 2581.3
## - alcohol 1 617.85 2715.1
## Start: AIC=2534.99
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 532.99 2534.1
## - fixed.acidity 1 533.07 2534.3
## - citric.acid 1 533.08 2534.3
## - density 1 533.22 2534.7
## <none> 532.53 2535.0
## - free.sulfur.dioxide 1 533.48 2535.3
## - pH 1 534.60 2538.0
## - chlorides 1 535.87 2541.0
## - total.sulfur.dioxide 1 537.58 2545.1
## - sulphates 1 553.65 2582.7
## - volatile.acidity 1 559.84 2597.0
## - alcohol 1 569.44 2618.7
##
## Step: AIC=2534.1
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + chlorides +
## free.sulfur.dioxide + total.sulfur.dioxide + density + pH +
## sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 533.24 2532.7
## - density 1 533.28 2532.8
## - citric.acid 1 533.48 2533.3
## <none> 532.99 2534.1
## - free.sulfur.dioxide 1 534.11 2534.8
## - pH 1 536.07 2539.5
## - chlorides 1 536.40 2540.2
## - total.sulfur.dioxide 1 537.90 2543.8
## - sulphates 1 553.70 2580.8
## - volatile.acidity 1 560.41 2596.2
## - alcohol 1 587.08 2655.7
##
## Step: AIC=2532.69
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 533.30 2530.8
## - citric.acid 1 533.56 2531.5
## <none> 533.24 2532.7
## - free.sulfur.dioxide 1 534.45 2533.6
## - chlorides 1 537.35 2540.5
## - total.sulfur.dioxide 1 539.40 2545.4
## - pH 1 541.38 2550.1
## - sulphates 1 553.73 2578.9
## - volatile.acidity 1 560.44 2594.3
## - alcohol 1 600.78 2683.2
##
## Step: AIC=2530.84
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 533.90 2530.3
## <none> 533.30 2530.8
## - free.sulfur.dioxide 1 534.49 2531.7
## - chlorides 1 537.36 2538.5
## - total.sulfur.dioxide 1 539.40 2543.4
## - pH 1 541.48 2548.3
## - sulphates 1 553.95 2577.4
## - volatile.acidity 1 563.66 2599.7
## - alcohol 1 636.04 2754.2
##
## Step: AIC=2530.29
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 533.90 2530.3
## - free.sulfur.dioxide 1 535.35 2531.8
## - chlorides 1 538.53 2539.3
## - total.sulfur.dioxide 1 540.74 2544.6
## - pH 1 541.96 2547.4
## - sulphates 1 554.11 2575.8
## - volatile.acidity 1 568.70 2609.0
## - alcohol 1 637.82 2755.8
## Start: AIC=3164.28
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 666.70 3163.0
## - fixed.acidity 1 666.80 3163.2
## - residual.sugar 1 666.91 3163.5
## - citric.acid 1 667.06 3163.8
## <none> 666.41 3164.3
## - free.sulfur.dioxide 1 668.10 3166.3
## - pH 1 668.37 3167.0
## - chlorides 1 674.80 3182.3
## - total.sulfur.dioxide 1 674.84 3182.4
## - sulphates 1 693.38 3225.7
## - volatile.acidity 1 700.03 3241.0
## - alcohol 1 712.08 3268.3
##
## Step: AIC=3162.96
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 666.81 3161.2
## - residual.sugar 1 666.93 3161.5
## - citric.acid 1 667.35 3162.5
## <none> 666.70 3163.0
## - free.sulfur.dioxide 1 668.53 3165.3
## - pH 1 671.02 3171.3
## - total.sulfur.dioxide 1 675.43 3181.8
## - chlorides 1 675.46 3181.8
## - sulphates 1 693.98 3225.1
## - volatile.acidity 1 701.70 3242.8
## - alcohol 1 786.37 3424.9
##
## Step: AIC=3161.22
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 667.06 3159.8
## - citric.acid 1 667.37 3160.6
## <none> 666.81 3161.2
## - free.sulfur.dioxide 1 668.71 3163.8
## - pH 1 673.87 3176.1
## - chlorides 1 676.75 3182.9
## - total.sulfur.dioxide 1 676.84 3183.1
## - sulphates 1 694.48 3224.2
## - volatile.acidity 1 703.04 3243.8
## - alcohol 1 787.44 3425.1
##
## Step: AIC=3159.84
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 667.54 3159.0
## <none> 667.06 3159.8
## - free.sulfur.dioxide 1 669.13 3162.8
## - pH 1 674.20 3174.9
## - total.sulfur.dioxide 1 676.89 3181.2
## - chlorides 1 676.89 3181.2
## - sulphates 1 694.51 3222.3
## - volatile.acidity 1 703.04 3241.8
## - alcohol 1 789.73 3427.8
##
## Step: AIC=3158.98
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 667.54 3159.0
## - free.sulfur.dioxide 1 669.93 3162.7
## - pH 1 674.61 3173.8
## - total.sulfur.dioxide 1 678.32 3182.6
## - chlorides 1 678.35 3182.7
## - sulphates 1 694.60 3220.5
## - volatile.acidity 1 709.85 3255.3
## - alcohol 1 792.02 3430.4
#model_stepwise
findCorrelation(
cor(df),
cutoff = 0.5,
verbose = TRUE,
names = TRUE
)
## Compare row 3 and column 1 with corr 0.672
## Means: 0.293 vs 0.19 so flagging column 3
## Compare row 1 and column 8 with corr 0.668
## Means: 0.245 vs 0.172 so flagging column 1
## Compare row 7 and column 6 with corr 0.668
## Means: 0.174 vs 0.169 so flagging column 7
## All correlations <= 0.5
## [1] "citric.acid" "fixed.acidity" "total.sulfur.dioxide"
ggcorrplot(correlation_df, hc.order = TRUE, type = "lower")
df_less_acid <- df %>%
select(-citric.acid, -fixed.acidity)
lm_less_acid <- lm(data = df_less_acid, quality ~ .)
summary(lm_less_acid)
##
## Call:
## lm(formula = quality ~ ., data = df_less_acid)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.66740 -0.37223 -0.04556 0.46264 2.03092
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.0575013 12.0089257 1.004 0.3155
## volatile.acidity -1.0127925 0.1009279 -10.035 < 2e-16 ***
## residual.sugar 0.0115046 0.0134606 0.855 0.3929
## chlorides -2.0490938 0.3992190 -5.133 3.21e-07 ***
## free.sulfur.dioxide 0.0048741 0.0021385 2.279 0.0228 *
## total.sulfur.dioxide -0.0035687 0.0006939 -5.143 3.03e-07 ***
## density -7.5668358 11.8648390 -0.638 0.5237
## pH -0.4919908 0.1210931 -4.063 5.08e-05 ***
## sulphates 0.9024434 0.1129657 7.989 2.60e-15 ***
## alcohol 0.2810022 0.0201992 13.912 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.648 on 1589 degrees of freedom
## Multiple R-squared: 0.3598, Adjusted R-squared: 0.3562
## F-statistic: 99.22 on 9 and 1589 DF, p-value: < 2.2e-16
plot(df)
colnames(df)
## [1] "fixed.acidity" "volatile.acidity" "citric.acid"
## [4] "residual.sugar" "chlorides" "free.sulfur.dioxide"
## [7] "total.sulfur.dioxide" "density" "pH"
## [10] "sulphates" "alcohol" "quality"
cols = c('fixed.acidity', 'volatile.acidity', 'citric.acid', 'residual.sugar', 'chlorides', 'free.sulfur.dioxide', 'total.sulfur.dioxide', 'density', 'pH', 'sulphates', 'alcohol')
pre_proc_val <- preProcess(train[,cols], method = c("center", "scale"))
train[,cols] = predict(pre_proc_val, train[,cols])
test[,cols] = predict(pre_proc_val, test[,cols])
summary(train)
## fixed.acidity volatile.acidity citric.acid residual.sugar
## Min. :-2.1641 Min. :-2.33694 Min. :-1.3873 Min. :-1.12033
## 1st Qu.:-0.7241 1st Qu.:-0.73547 1st Qu.:-0.8734 1st Qu.:-0.44605
## Median :-0.2633 Median :-0.04912 Median :-0.1026 Median :-0.24377
## Mean : 0.0000 Mean : 0.00000 Mean : 0.0000 Mean : 0.00000
## 3rd Qu.: 0.5431 3rd Qu.: 0.63723 3rd Qu.: 0.7711 3rd Qu.: 0.02594
## Max. : 4.1143 Max. : 6.01361 Max. : 2.6726 Max. : 8.65665
## chlorides free.sulfur.dioxide total.sulfur.dioxide
## Min. :-1.74737 Min. :-1.4241 Min. :-1.2284
## 1st Qu.:-0.37937 1st Qu.:-0.7606 1st Qu.:-0.7423
## Median :-0.19388 Median :-0.1919 Median :-0.2561
## Mean : 0.00000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.08435 3rd Qu.: 0.5190 3rd Qu.: 0.4731
## Max. : 8.80242 Max. : 5.3056 Max. : 7.3704
## density pH sulphates alcohol
## Min. :-3.541362 Min. :-2.930364 Min. :-2.0708 Min. :-1.8774
## 1st Qu.:-0.605231 1st Qu.:-0.655529 1st Qu.:-0.6664 1st Qu.:-0.8516
## Median :-0.006449 Median :-0.005576 Median :-0.2195 Median :-0.2920
## Mean : 0.000000 Mean : 0.000000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.571322 3rd Qu.: 0.579382 3rd Qu.: 0.4827 3rd Qu.: 0.5473
## Max. : 3.612502 Max. : 4.544094 Max. : 8.2710 Max. : 3.3449
## quality
## Min. :3.000
## 1st Qu.:5.000
## Median :6.000
## Mean :5.636
## 3rd Qu.:6.000
## Max. :8.000
#generic LM
lm_2 <- lm(quality ~ ., data = train)
summary(lm_2)
##
## Call:
## lm(formula = quality ~ ., data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.71239 -0.36588 -0.05802 0.45321 1.92777
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.63628 0.01935 291.341 < 2e-16 ***
## fixed.acidity 0.07057 0.05421 1.302 0.19324
## volatile.acidity -0.16270 0.02571 -6.328 3.60e-10 ***
## citric.acid -0.04640 0.03435 -1.351 0.17703
## residual.sugar 0.05101 0.02553 1.998 0.04597 *
## chlorides -0.06809 0.02356 -2.890 0.00393 **
## free.sulfur.dioxide 0.05923 0.02722 2.175 0.02980 *
## total.sulfur.dioxide -0.11349 0.02851 -3.980 7.33e-05 ***
## density -0.08224 0.04845 -1.697 0.08992 .
## pH -0.07915 0.03526 -2.245 0.02498 *
## sulphates 0.16221 0.02295 7.067 2.79e-12 ***
## alcohol 0.27958 0.03289 8.500 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6472 on 1107 degrees of freedom
## Multiple R-squared: 0.3461, Adjusted R-squared: 0.3396
## F-statistic: 53.26 on 11 and 1107 DF, p-value: < 2.2e-16
cols_reg = c('fixed.acidity', 'volatile.acidity', 'citric.acid', 'residual.sugar', 'chlorides', 'free.sulfur.dioxide', 'total.sulfur.dioxide', 'density', 'pH', 'sulphates', 'alcohol', 'quality')
dummies <- dummyVars(quality ~ ., data = df[,cols_reg])
train_dummies = predict(dummies, newdata = train[,cols_reg])
test_dummies = predict(dummies, newdata = test[,cols_reg])
print(dim(train_dummies)); print(dim(test_dummies))
## [1] 1119 11
## [1] 480 11
x = as.matrix(train_dummies)
y_train = train$quality
x_test = as.matrix(test_dummies)
y_test = test$quality
lambdas <- 10^seq(2, -3, by = -.1)
ridge_reg = glmnet(x, y_train, nlambda = 25, alpha = 0, family = 'gaussian', lambda = lambdas)
summary(ridge_reg)
## Length Class Mode
## a0 51 -none- numeric
## beta 561 dgCMatrix S4
## df 51 -none- numeric
## dim 2 -none- numeric
## lambda 51 -none- numeric
## dev.ratio 51 -none- numeric
## nulldev 1 -none- numeric
## npasses 1 -none- numeric
## jerr 1 -none- numeric
## offset 1 -none- logical
## call 7 -none- call
## nobs 1 -none- numeric
cv_ridge <- cv.glmnet(x, y_train, alpha = 0, lambda = lambdas)
optimal_lambda <- cv_ridge$lambda.min
optimal_lambda
## [1] 0.03981072
# Compute R^2 from true and predicted values
eval_results <- function(true, predicted, df) {
SSE <- sum((predicted - true)^2)
SST <- sum((true - mean(true))^2)
R_square <- 1 - SSE / SST
RMSE = sqrt(SSE/nrow(df))
# Model performance metrics
data.frame(
RMSE = RMSE,
Rsquare = R_square
)
}
# Prediction and evaluation on train data
predictions_train <- predict(ridge_reg, s = optimal_lambda, newx = x)
eval_results(y_train, predictions_train, train)
## RMSE Rsquare
## 1 0.6440413 0.3453163
# Prediction and evaluation on test data
predictions_test <- predict(ridge_reg, s = optimal_lambda, newx = x_test)
eval_results(y_test, predictions_test, test)
## RMSE Rsquare
## 1 0.6553348 0.381321
lambdas <- 10^seq(2, -3, by = -.1)
# Setting alpha = 1 implements lasso regression
lasso_reg <- cv.glmnet(x, y_train, alpha = 1, lambda = lambdas, standardize = TRUE, nfolds = 5)
# Best
lambda_best <- lasso_reg$lambda.min
lambda_best
## [1] 0.001
lasso_model <- glmnet(x, y_train, alpha = 1, lambda = lambda_best, standardize = TRUE)
predictions_train <- predict(lasso_model, s = lambda_best, newx = x)
eval_results(y_train, predictions_train, train)
## RMSE Rsquare
## 1 0.6436934 0.3460234
predictions_test <- predict(lasso_model, s = lambda_best, newx = x_test)
eval_results(y_test, predictions_test, test)
## RMSE Rsquare
## 1 0.6553293 0.3813313
# Set training control
train_cont <- trainControl(method = "repeatedcv",
number = 10,
repeats = 5,
search = "random",
verboseIter = TRUE)
# Train the model
elastic_reg <- train(quality ~ .,
data = train,
method = "glmnet",
preProcess = c("center", "scale"),
tuneLength = 10,
trControl = train_cont)
## + Fold01.Rep1: alpha=0.7034, lambda=0.215777
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## + Fold01.Rep1: alpha=0.1303, lambda=2.918438
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## + Fold01.Rep1: alpha=0.9303, lambda=0.013567
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## + Fold01.Rep1: alpha=0.9076, lambda=3.206257
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## + Fold01.Rep1: alpha=0.3536, lambda=3.736772
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## + Fold01.Rep1: alpha=0.7569, lambda=0.457474
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## + Fold01.Rep1: alpha=0.4423, lambda=0.004959
## - Fold01.Rep1: alpha=0.4423, lambda=0.004959
## + Fold01.Rep1: alpha=0.4111, lambda=0.885269
## - Fold01.Rep1: alpha=0.4111, lambda=0.885269
## + Fold01.Rep1: alpha=0.4419, lambda=0.014470
## - Fold01.Rep1: alpha=0.4419, lambda=0.014470
## + Fold01.Rep1: alpha=0.2539, lambda=6.506213
## - Fold01.Rep1: alpha=0.2539, lambda=6.506213
## + Fold02.Rep1: alpha=0.7034, lambda=0.215777
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## + Fold02.Rep1: alpha=0.1303, lambda=2.918438
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## + Fold02.Rep1: alpha=0.9303, lambda=0.013567
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## + Fold02.Rep1: alpha=0.9076, lambda=3.206257
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## + Fold02.Rep1: alpha=0.3536, lambda=3.736772
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## + Fold02.Rep1: alpha=0.7569, lambda=0.457474
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## + Fold02.Rep1: alpha=0.4423, lambda=0.004959
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## + Fold02.Rep1: alpha=0.4111, lambda=0.885269
## - Fold02.Rep1: alpha=0.4111, lambda=0.885269
## + Fold02.Rep1: alpha=0.4419, lambda=0.014470
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## + Fold02.Rep1: alpha=0.2539, lambda=6.506213
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## + Fold03.Rep1: alpha=0.7034, lambda=0.215777
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## + Fold03.Rep1: alpha=0.1303, lambda=2.918438
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## + Fold03.Rep1: alpha=0.9303, lambda=0.013567
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## + Fold03.Rep1: alpha=0.9076, lambda=3.206257
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## + Fold03.Rep1: alpha=0.3536, lambda=3.736772
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## + Fold03.Rep1: alpha=0.7569, lambda=0.457474
## - Fold03.Rep1: alpha=0.7569, lambda=0.457474
## + Fold03.Rep1: alpha=0.4423, lambda=0.004959
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## + Fold03.Rep1: alpha=0.4111, lambda=0.885269
## - Fold03.Rep1: alpha=0.4111, lambda=0.885269
## + Fold03.Rep1: alpha=0.4419, lambda=0.014470
## - Fold03.Rep1: alpha=0.4419, lambda=0.014470
## + Fold03.Rep1: alpha=0.2539, lambda=6.506213
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## + Fold04.Rep1: alpha=0.1303, lambda=2.918438
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## + Fold04.Rep1: alpha=0.9303, lambda=0.013567
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## + Fold04.Rep1: alpha=0.9076, lambda=3.206257
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## + Fold04.Rep1: alpha=0.3536, lambda=3.736772
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## + Fold04.Rep1: alpha=0.7569, lambda=0.457474
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## + Fold04.Rep1: alpha=0.4423, lambda=0.004959
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## + Fold04.Rep1: alpha=0.4111, lambda=0.885269
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## + Fold04.Rep1: alpha=0.4419, lambda=0.014470
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## + Fold04.Rep1: alpha=0.2539, lambda=6.506213
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## + Fold05.Rep1: alpha=0.1303, lambda=2.918438
## - Fold05.Rep1: alpha=0.1303, lambda=2.918438
## + Fold05.Rep1: alpha=0.9303, lambda=0.013567
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## + Fold05.Rep1: alpha=0.9076, lambda=3.206257
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## + Fold05.Rep1: alpha=0.3536, lambda=3.736772
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## + Fold05.Rep1: alpha=0.7569, lambda=0.457474
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## + Fold05.Rep1: alpha=0.4423, lambda=0.004959
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## + Fold05.Rep1: alpha=0.4111, lambda=0.885269
## - Fold05.Rep1: alpha=0.4111, lambda=0.885269
## + Fold05.Rep1: alpha=0.4419, lambda=0.014470
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## + Fold05.Rep1: alpha=0.2539, lambda=6.506213
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## + Fold06.Rep1: alpha=0.9303, lambda=0.013567
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## + Fold06.Rep1: alpha=0.9076, lambda=3.206257
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## + Fold06.Rep1: alpha=0.3536, lambda=3.736772
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## + Fold06.Rep1: alpha=0.7569, lambda=0.457474
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## + Fold06.Rep1: alpha=0.4423, lambda=0.004959
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## + Fold06.Rep1: alpha=0.4111, lambda=0.885269
## - Fold06.Rep1: alpha=0.4111, lambda=0.885269
## + Fold06.Rep1: alpha=0.4419, lambda=0.014470
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## + Fold06.Rep1: alpha=0.2539, lambda=6.506213
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## + Fold07.Rep1: alpha=0.7034, lambda=0.215777
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## + Fold07.Rep1: alpha=0.1303, lambda=2.918438
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## + Fold07.Rep1: alpha=0.4419, lambda=0.014470
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## + Fold07.Rep1: alpha=0.2539, lambda=6.506213
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## + Fold08.Rep1: alpha=0.4423, lambda=0.004959
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## + Fold08.Rep1: alpha=0.4111, lambda=0.885269
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## + Fold08.Rep1: alpha=0.4419, lambda=0.014470
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## + Fold08.Rep1: alpha=0.2539, lambda=6.506213
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## + Fold10.Rep1: alpha=0.7034, lambda=0.215777
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## + Fold10.Rep1: alpha=0.1303, lambda=2.918438
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## + Fold10.Rep1: alpha=0.9303, lambda=0.013567
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## + Fold10.Rep1: alpha=0.4423, lambda=0.004959
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## + Fold10.Rep1: alpha=0.4111, lambda=0.885269
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## + Fold10.Rep1: alpha=0.4419, lambda=0.014470
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## + Fold10.Rep1: alpha=0.2539, lambda=6.506213
## - Fold10.Rep1: alpha=0.2539, lambda=6.506213
## + Fold01.Rep2: alpha=0.7034, lambda=0.215777
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## + Fold01.Rep2: alpha=0.1303, lambda=2.918438
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## + Fold01.Rep2: alpha=0.9303, lambda=0.013567
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## + Fold01.Rep2: alpha=0.9076, lambda=3.206257
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## + Fold01.Rep2: alpha=0.3536, lambda=3.736772
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## + Fold01.Rep2: alpha=0.7569, lambda=0.457474
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## + Fold01.Rep2: alpha=0.4423, lambda=0.004959
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## + Fold01.Rep2: alpha=0.4111, lambda=0.885269
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## + Fold01.Rep2: alpha=0.4419, lambda=0.014470
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## + Fold01.Rep2: alpha=0.2539, lambda=6.506213
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## + Fold02.Rep2: alpha=0.7034, lambda=0.215777
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## + Fold02.Rep2: alpha=0.1303, lambda=2.918438
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## + Fold02.Rep2: alpha=0.9303, lambda=0.013567
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## + Fold02.Rep2: alpha=0.3536, lambda=3.736772
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## + Fold02.Rep2: alpha=0.7569, lambda=0.457474
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## + Fold02.Rep2: alpha=0.4423, lambda=0.004959
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## + Fold02.Rep2: alpha=0.4111, lambda=0.885269
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## + Fold02.Rep2: alpha=0.4419, lambda=0.014470
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## + Fold02.Rep2: alpha=0.2539, lambda=6.506213
## - Fold02.Rep2: alpha=0.2539, lambda=6.506213
## + Fold03.Rep2: alpha=0.7034, lambda=0.215777
## - Fold03.Rep2: alpha=0.7034, lambda=0.215777
## + Fold03.Rep2: alpha=0.1303, lambda=2.918438
## - Fold03.Rep2: alpha=0.1303, lambda=2.918438
## + Fold03.Rep2: alpha=0.9303, lambda=0.013567
## - Fold03.Rep2: alpha=0.9303, lambda=0.013567
## + Fold03.Rep2: alpha=0.9076, lambda=3.206257
## - Fold03.Rep2: alpha=0.9076, lambda=3.206257
## + Fold03.Rep2: alpha=0.3536, lambda=3.736772
## - Fold03.Rep2: alpha=0.3536, lambda=3.736772
## + Fold03.Rep2: alpha=0.7569, lambda=0.457474
## - Fold03.Rep2: alpha=0.7569, lambda=0.457474
## + Fold03.Rep2: alpha=0.4423, lambda=0.004959
## - Fold03.Rep2: alpha=0.4423, lambda=0.004959
## + Fold03.Rep2: alpha=0.4111, lambda=0.885269
## - Fold03.Rep2: alpha=0.4111, lambda=0.885269
## + Fold03.Rep2: alpha=0.4419, lambda=0.014470
## - Fold03.Rep2: alpha=0.4419, lambda=0.014470
## + Fold03.Rep2: alpha=0.2539, lambda=6.506213
## - Fold03.Rep2: alpha=0.2539, lambda=6.506213
## + Fold04.Rep2: alpha=0.7034, lambda=0.215777
## - Fold04.Rep2: alpha=0.7034, lambda=0.215777
## + Fold04.Rep2: alpha=0.1303, lambda=2.918438
## - Fold04.Rep2: alpha=0.1303, lambda=2.918438
## + Fold04.Rep2: alpha=0.9303, lambda=0.013567
## - Fold04.Rep2: alpha=0.9303, lambda=0.013567
## + Fold04.Rep2: alpha=0.9076, lambda=3.206257
## - Fold04.Rep2: alpha=0.9076, lambda=3.206257
## + Fold04.Rep2: alpha=0.3536, lambda=3.736772
## - Fold04.Rep2: alpha=0.3536, lambda=3.736772
## + Fold04.Rep2: alpha=0.7569, lambda=0.457474
## - Fold04.Rep2: alpha=0.7569, lambda=0.457474
## + Fold04.Rep2: alpha=0.4423, lambda=0.004959
## - Fold04.Rep2: alpha=0.4423, lambda=0.004959
## + Fold04.Rep2: alpha=0.4111, lambda=0.885269
## - Fold04.Rep2: alpha=0.4111, lambda=0.885269
## + Fold04.Rep2: alpha=0.4419, lambda=0.014470
## - Fold04.Rep2: alpha=0.4419, lambda=0.014470
## + Fold04.Rep2: alpha=0.2539, lambda=6.506213
## - Fold04.Rep2: alpha=0.2539, lambda=6.506213
## + Fold05.Rep2: alpha=0.7034, lambda=0.215777
## - Fold05.Rep2: alpha=0.7034, lambda=0.215777
## + Fold05.Rep2: alpha=0.1303, lambda=2.918438
## - Fold05.Rep2: alpha=0.1303, lambda=2.918438
## + Fold05.Rep2: alpha=0.9303, lambda=0.013567
## - Fold05.Rep2: alpha=0.9303, lambda=0.013567
## + Fold05.Rep2: alpha=0.9076, lambda=3.206257
## - Fold05.Rep2: alpha=0.9076, lambda=3.206257
## + Fold05.Rep2: alpha=0.3536, lambda=3.736772
## - Fold05.Rep2: alpha=0.3536, lambda=3.736772
## + Fold05.Rep2: alpha=0.7569, lambda=0.457474
## - Fold05.Rep2: alpha=0.7569, lambda=0.457474
## + Fold05.Rep2: alpha=0.4423, lambda=0.004959
## - Fold05.Rep2: alpha=0.4423, lambda=0.004959
## + Fold05.Rep2: alpha=0.4111, lambda=0.885269
## - Fold05.Rep2: alpha=0.4111, lambda=0.885269
## + Fold05.Rep2: alpha=0.4419, lambda=0.014470
## - Fold05.Rep2: alpha=0.4419, lambda=0.014470
## + Fold05.Rep2: alpha=0.2539, lambda=6.506213
## - Fold05.Rep2: alpha=0.2539, lambda=6.506213
## + Fold06.Rep2: alpha=0.7034, lambda=0.215777
## - Fold06.Rep2: alpha=0.7034, lambda=0.215777
## + Fold06.Rep2: alpha=0.1303, lambda=2.918438
## - Fold06.Rep2: alpha=0.1303, lambda=2.918438
## + Fold06.Rep2: alpha=0.9303, lambda=0.013567
## - Fold06.Rep2: alpha=0.9303, lambda=0.013567
## + Fold06.Rep2: alpha=0.9076, lambda=3.206257
## - Fold06.Rep2: alpha=0.9076, lambda=3.206257
## + Fold06.Rep2: alpha=0.3536, lambda=3.736772
## - Fold06.Rep2: alpha=0.3536, lambda=3.736772
## + Fold06.Rep2: alpha=0.7569, lambda=0.457474
## - Fold06.Rep2: alpha=0.7569, lambda=0.457474
## + Fold06.Rep2: alpha=0.4423, lambda=0.004959
## - Fold06.Rep2: alpha=0.4423, lambda=0.004959
## + Fold06.Rep2: alpha=0.4111, lambda=0.885269
## - Fold06.Rep2: alpha=0.4111, lambda=0.885269
## + Fold06.Rep2: alpha=0.4419, lambda=0.014470
## - Fold06.Rep2: alpha=0.4419, lambda=0.014470
## + Fold06.Rep2: alpha=0.2539, lambda=6.506213
## - Fold06.Rep2: alpha=0.2539, lambda=6.506213
## + Fold07.Rep2: alpha=0.7034, lambda=0.215777
## - Fold07.Rep2: alpha=0.7034, lambda=0.215777
## + Fold07.Rep2: alpha=0.1303, lambda=2.918438
## - Fold07.Rep2: alpha=0.1303, lambda=2.918438
## + Fold07.Rep2: alpha=0.9303, lambda=0.013567
## - Fold07.Rep2: alpha=0.9303, lambda=0.013567
## + Fold07.Rep2: alpha=0.9076, lambda=3.206257
## - Fold07.Rep2: alpha=0.9076, lambda=3.206257
## + Fold07.Rep2: alpha=0.3536, lambda=3.736772
## - Fold07.Rep2: alpha=0.3536, lambda=3.736772
## + Fold07.Rep2: alpha=0.7569, lambda=0.457474
## - Fold07.Rep2: alpha=0.7569, lambda=0.457474
## + Fold07.Rep2: alpha=0.4423, lambda=0.004959
## - Fold07.Rep2: alpha=0.4423, lambda=0.004959
## + Fold07.Rep2: alpha=0.4111, lambda=0.885269
## - Fold07.Rep2: alpha=0.4111, lambda=0.885269
## + Fold07.Rep2: alpha=0.4419, lambda=0.014470
## - Fold07.Rep2: alpha=0.4419, lambda=0.014470
## + Fold07.Rep2: alpha=0.2539, lambda=6.506213
## - Fold07.Rep2: alpha=0.2539, lambda=6.506213
## + Fold08.Rep2: alpha=0.7034, lambda=0.215777
## - Fold08.Rep2: alpha=0.7034, lambda=0.215777
## + Fold08.Rep2: alpha=0.1303, lambda=2.918438
## - Fold08.Rep2: alpha=0.1303, lambda=2.918438
## + Fold08.Rep2: alpha=0.9303, lambda=0.013567
## - Fold08.Rep2: alpha=0.9303, lambda=0.013567
## + Fold08.Rep2: alpha=0.9076, lambda=3.206257
## - Fold08.Rep2: alpha=0.9076, lambda=3.206257
## + Fold08.Rep2: alpha=0.3536, lambda=3.736772
## - Fold08.Rep2: alpha=0.3536, lambda=3.736772
## + Fold08.Rep2: alpha=0.7569, lambda=0.457474
## - Fold08.Rep2: alpha=0.7569, lambda=0.457474
## + Fold08.Rep2: alpha=0.4423, lambda=0.004959
## - Fold08.Rep2: alpha=0.4423, lambda=0.004959
## + Fold08.Rep2: alpha=0.4111, lambda=0.885269
## - Fold08.Rep2: alpha=0.4111, lambda=0.885269
## + Fold08.Rep2: alpha=0.4419, lambda=0.014470
## - Fold08.Rep2: alpha=0.4419, lambda=0.014470
## + Fold08.Rep2: alpha=0.2539, lambda=6.506213
## - Fold08.Rep2: alpha=0.2539, lambda=6.506213
## + Fold09.Rep2: alpha=0.7034, lambda=0.215777
## - Fold09.Rep2: alpha=0.7034, lambda=0.215777
## + Fold09.Rep2: alpha=0.1303, lambda=2.918438
## - Fold09.Rep2: alpha=0.1303, lambda=2.918438
## + Fold09.Rep2: alpha=0.9303, lambda=0.013567
## - Fold09.Rep2: alpha=0.9303, lambda=0.013567
## + Fold09.Rep2: alpha=0.9076, lambda=3.206257
## - Fold09.Rep2: alpha=0.9076, lambda=3.206257
## + Fold09.Rep2: alpha=0.3536, lambda=3.736772
## - Fold09.Rep2: alpha=0.3536, lambda=3.736772
## + Fold09.Rep2: alpha=0.7569, lambda=0.457474
## - Fold09.Rep2: alpha=0.7569, lambda=0.457474
## + Fold09.Rep2: alpha=0.4423, lambda=0.004959
## - Fold09.Rep2: alpha=0.4423, lambda=0.004959
## + Fold09.Rep2: alpha=0.4111, lambda=0.885269
## - Fold09.Rep2: alpha=0.4111, lambda=0.885269
## + Fold09.Rep2: alpha=0.4419, lambda=0.014470
## - Fold09.Rep2: alpha=0.4419, lambda=0.014470
## + Fold09.Rep2: alpha=0.2539, lambda=6.506213
## - Fold09.Rep2: alpha=0.2539, lambda=6.506213
## + Fold10.Rep2: alpha=0.7034, lambda=0.215777
## - Fold10.Rep2: alpha=0.7034, lambda=0.215777
## + Fold10.Rep2: alpha=0.1303, lambda=2.918438
## - Fold10.Rep2: alpha=0.1303, lambda=2.918438
## + Fold10.Rep2: alpha=0.9303, lambda=0.013567
## - Fold10.Rep2: alpha=0.9303, lambda=0.013567
## + Fold10.Rep2: alpha=0.9076, lambda=3.206257
## - Fold10.Rep2: alpha=0.9076, lambda=3.206257
## + Fold10.Rep2: alpha=0.3536, lambda=3.736772
## - Fold10.Rep2: alpha=0.3536, lambda=3.736772
## + Fold10.Rep2: alpha=0.7569, lambda=0.457474
## - Fold10.Rep2: alpha=0.7569, lambda=0.457474
## + Fold10.Rep2: alpha=0.4423, lambda=0.004959
## - Fold10.Rep2: alpha=0.4423, lambda=0.004959
## + Fold10.Rep2: alpha=0.4111, lambda=0.885269
## - Fold10.Rep2: alpha=0.4111, lambda=0.885269
## + Fold10.Rep2: alpha=0.4419, lambda=0.014470
## - Fold10.Rep2: alpha=0.4419, lambda=0.014470
## + Fold10.Rep2: alpha=0.2539, lambda=6.506213
## - Fold10.Rep2: alpha=0.2539, lambda=6.506213
## + Fold01.Rep3: alpha=0.7034, lambda=0.215777
## - Fold01.Rep3: alpha=0.7034, lambda=0.215777
## + Fold01.Rep3: alpha=0.1303, lambda=2.918438
## - Fold01.Rep3: alpha=0.1303, lambda=2.918438
## + Fold01.Rep3: alpha=0.9303, lambda=0.013567
## - Fold01.Rep3: alpha=0.9303, lambda=0.013567
## + Fold01.Rep3: alpha=0.9076, lambda=3.206257
## - Fold01.Rep3: alpha=0.9076, lambda=3.206257
## + Fold01.Rep3: alpha=0.3536, lambda=3.736772
## - Fold01.Rep3: alpha=0.3536, lambda=3.736772
## + Fold01.Rep3: alpha=0.7569, lambda=0.457474
## - Fold01.Rep3: alpha=0.7569, lambda=0.457474
## + Fold01.Rep3: alpha=0.4423, lambda=0.004959
## - Fold01.Rep3: alpha=0.4423, lambda=0.004959
## + Fold01.Rep3: alpha=0.4111, lambda=0.885269
## - Fold01.Rep3: alpha=0.4111, lambda=0.885269
## + Fold01.Rep3: alpha=0.4419, lambda=0.014470
## - Fold01.Rep3: alpha=0.4419, lambda=0.014470
## + Fold01.Rep3: alpha=0.2539, lambda=6.506213
## - Fold01.Rep3: alpha=0.2539, lambda=6.506213
## + Fold02.Rep3: alpha=0.7034, lambda=0.215777
## - Fold02.Rep3: alpha=0.7034, lambda=0.215777
## + Fold02.Rep3: alpha=0.1303, lambda=2.918438
## - Fold02.Rep3: alpha=0.1303, lambda=2.918438
## + Fold02.Rep3: alpha=0.9303, lambda=0.013567
## - Fold02.Rep3: alpha=0.9303, lambda=0.013567
## + Fold02.Rep3: alpha=0.9076, lambda=3.206257
## - Fold02.Rep3: alpha=0.9076, lambda=3.206257
## + Fold02.Rep3: alpha=0.3536, lambda=3.736772
## - Fold02.Rep3: alpha=0.3536, lambda=3.736772
## + Fold02.Rep3: alpha=0.7569, lambda=0.457474
## - Fold02.Rep3: alpha=0.7569, lambda=0.457474
## + Fold02.Rep3: alpha=0.4423, lambda=0.004959
## - Fold02.Rep3: alpha=0.4423, lambda=0.004959
## + Fold02.Rep3: alpha=0.4111, lambda=0.885269
## - Fold02.Rep3: alpha=0.4111, lambda=0.885269
## + Fold02.Rep3: alpha=0.4419, lambda=0.014470
## - Fold02.Rep3: alpha=0.4419, lambda=0.014470
## + Fold02.Rep3: alpha=0.2539, lambda=6.506213
## - Fold02.Rep3: alpha=0.2539, lambda=6.506213
## + Fold03.Rep3: alpha=0.7034, lambda=0.215777
## - Fold03.Rep3: alpha=0.7034, lambda=0.215777
## + Fold03.Rep3: alpha=0.1303, lambda=2.918438
## - Fold03.Rep3: alpha=0.1303, lambda=2.918438
## + Fold03.Rep3: alpha=0.9303, lambda=0.013567
## - Fold03.Rep3: alpha=0.9303, lambda=0.013567
## + Fold03.Rep3: alpha=0.9076, lambda=3.206257
## - Fold03.Rep3: alpha=0.9076, lambda=3.206257
## + Fold03.Rep3: alpha=0.3536, lambda=3.736772
## - Fold03.Rep3: alpha=0.3536, lambda=3.736772
## + Fold03.Rep3: alpha=0.7569, lambda=0.457474
## - Fold03.Rep3: alpha=0.7569, lambda=0.457474
## + Fold03.Rep3: alpha=0.4423, lambda=0.004959
## - Fold03.Rep3: alpha=0.4423, lambda=0.004959
## + Fold03.Rep3: alpha=0.4111, lambda=0.885269
## - Fold03.Rep3: alpha=0.4111, lambda=0.885269
## + Fold03.Rep3: alpha=0.4419, lambda=0.014470
## - Fold03.Rep3: alpha=0.4419, lambda=0.014470
## + Fold03.Rep3: alpha=0.2539, lambda=6.506213
## - Fold03.Rep3: alpha=0.2539, lambda=6.506213
## + Fold04.Rep3: alpha=0.7034, lambda=0.215777
## - Fold04.Rep3: alpha=0.7034, lambda=0.215777
## + Fold04.Rep3: alpha=0.1303, lambda=2.918438
## - Fold04.Rep3: alpha=0.1303, lambda=2.918438
## + Fold04.Rep3: alpha=0.9303, lambda=0.013567
## - Fold04.Rep3: alpha=0.9303, lambda=0.013567
## + Fold04.Rep3: alpha=0.9076, lambda=3.206257
## - Fold04.Rep3: alpha=0.9076, lambda=3.206257
## + Fold04.Rep3: alpha=0.3536, lambda=3.736772
## - Fold04.Rep3: alpha=0.3536, lambda=3.736772
## + Fold04.Rep3: alpha=0.7569, lambda=0.457474
## - Fold04.Rep3: alpha=0.7569, lambda=0.457474
## + Fold04.Rep3: alpha=0.4423, lambda=0.004959
## - Fold04.Rep3: alpha=0.4423, lambda=0.004959
## + Fold04.Rep3: alpha=0.4111, lambda=0.885269
## - Fold04.Rep3: alpha=0.4111, lambda=0.885269
## + Fold04.Rep3: alpha=0.4419, lambda=0.014470
## - Fold04.Rep3: alpha=0.4419, lambda=0.014470
## + Fold04.Rep3: alpha=0.2539, lambda=6.506213
## - Fold04.Rep3: alpha=0.2539, lambda=6.506213
## + Fold05.Rep3: alpha=0.7034, lambda=0.215777
## - Fold05.Rep3: alpha=0.7034, lambda=0.215777
## + Fold05.Rep3: alpha=0.1303, lambda=2.918438
## - Fold05.Rep3: alpha=0.1303, lambda=2.918438
## + Fold05.Rep3: alpha=0.9303, lambda=0.013567
## - Fold05.Rep3: alpha=0.9303, lambda=0.013567
## + Fold05.Rep3: alpha=0.9076, lambda=3.206257
## - Fold05.Rep3: alpha=0.9076, lambda=3.206257
## + Fold05.Rep3: alpha=0.3536, lambda=3.736772
## - Fold05.Rep3: alpha=0.3536, lambda=3.736772
## + Fold05.Rep3: alpha=0.7569, lambda=0.457474
## - Fold05.Rep3: alpha=0.7569, lambda=0.457474
## + Fold05.Rep3: alpha=0.4423, lambda=0.004959
## - Fold05.Rep3: alpha=0.4423, lambda=0.004959
## + Fold05.Rep3: alpha=0.4111, lambda=0.885269
## - Fold05.Rep3: alpha=0.4111, lambda=0.885269
## + Fold05.Rep3: alpha=0.4419, lambda=0.014470
## - Fold05.Rep3: alpha=0.4419, lambda=0.014470
## + Fold05.Rep3: alpha=0.2539, lambda=6.506213
## - Fold05.Rep3: alpha=0.2539, lambda=6.506213
## + Fold06.Rep3: alpha=0.7034, lambda=0.215777
## - Fold06.Rep3: alpha=0.7034, lambda=0.215777
## + Fold06.Rep3: alpha=0.1303, lambda=2.918438
## - Fold06.Rep3: alpha=0.1303, lambda=2.918438
## + Fold06.Rep3: alpha=0.9303, lambda=0.013567
## - Fold06.Rep3: alpha=0.9303, lambda=0.013567
## + Fold06.Rep3: alpha=0.9076, lambda=3.206257
## - Fold06.Rep3: alpha=0.9076, lambda=3.206257
## + Fold06.Rep3: alpha=0.3536, lambda=3.736772
## - Fold06.Rep3: alpha=0.3536, lambda=3.736772
## + Fold06.Rep3: alpha=0.7569, lambda=0.457474
## - Fold06.Rep3: alpha=0.7569, lambda=0.457474
## + Fold06.Rep3: alpha=0.4423, lambda=0.004959
## - Fold06.Rep3: alpha=0.4423, lambda=0.004959
## + Fold06.Rep3: alpha=0.4111, lambda=0.885269
## - Fold06.Rep3: alpha=0.4111, lambda=0.885269
## + Fold06.Rep3: alpha=0.4419, lambda=0.014470
## - Fold06.Rep3: alpha=0.4419, lambda=0.014470
## + Fold06.Rep3: alpha=0.2539, lambda=6.506213
## - Fold06.Rep3: alpha=0.2539, lambda=6.506213
## + Fold07.Rep3: alpha=0.7034, lambda=0.215777
## - Fold07.Rep3: alpha=0.7034, lambda=0.215777
## + Fold07.Rep3: alpha=0.1303, lambda=2.918438
## - Fold07.Rep3: alpha=0.1303, lambda=2.918438
## + Fold07.Rep3: alpha=0.9303, lambda=0.013567
## - Fold07.Rep3: alpha=0.9303, lambda=0.013567
## + Fold07.Rep3: alpha=0.9076, lambda=3.206257
## - Fold07.Rep3: alpha=0.9076, lambda=3.206257
## + Fold07.Rep3: alpha=0.3536, lambda=3.736772
## - Fold07.Rep3: alpha=0.3536, lambda=3.736772
## + Fold07.Rep3: alpha=0.7569, lambda=0.457474
## - Fold07.Rep3: alpha=0.7569, lambda=0.457474
## + Fold07.Rep3: alpha=0.4423, lambda=0.004959
## - Fold07.Rep3: alpha=0.4423, lambda=0.004959
## + Fold07.Rep3: alpha=0.4111, lambda=0.885269
## - Fold07.Rep3: alpha=0.4111, lambda=0.885269
## + Fold07.Rep3: alpha=0.4419, lambda=0.014470
## - Fold07.Rep3: alpha=0.4419, lambda=0.014470
## + Fold07.Rep3: alpha=0.2539, lambda=6.506213
## - Fold07.Rep3: alpha=0.2539, lambda=6.506213
## + Fold08.Rep3: alpha=0.7034, lambda=0.215777
## - Fold08.Rep3: alpha=0.7034, lambda=0.215777
## + Fold08.Rep3: alpha=0.1303, lambda=2.918438
## - Fold08.Rep3: alpha=0.1303, lambda=2.918438
## + Fold08.Rep3: alpha=0.9303, lambda=0.013567
## - Fold08.Rep3: alpha=0.9303, lambda=0.013567
## + Fold08.Rep3: alpha=0.9076, lambda=3.206257
## - Fold08.Rep3: alpha=0.9076, lambda=3.206257
## + Fold08.Rep3: alpha=0.3536, lambda=3.736772
## - Fold08.Rep3: alpha=0.3536, lambda=3.736772
## + Fold08.Rep3: alpha=0.7569, lambda=0.457474
## - Fold08.Rep3: alpha=0.7569, lambda=0.457474
## + Fold08.Rep3: alpha=0.4423, lambda=0.004959
## - Fold08.Rep3: alpha=0.4423, lambda=0.004959
## + Fold08.Rep3: alpha=0.4111, lambda=0.885269
## - Fold08.Rep3: alpha=0.4111, lambda=0.885269
## + Fold08.Rep3: alpha=0.4419, lambda=0.014470
## - Fold08.Rep3: alpha=0.4419, lambda=0.014470
## + Fold08.Rep3: alpha=0.2539, lambda=6.506213
## - Fold08.Rep3: alpha=0.2539, lambda=6.506213
## + Fold09.Rep3: alpha=0.7034, lambda=0.215777
## - Fold09.Rep3: alpha=0.7034, lambda=0.215777
## + Fold09.Rep3: alpha=0.1303, lambda=2.918438
## - Fold09.Rep3: alpha=0.1303, lambda=2.918438
## + Fold09.Rep3: alpha=0.9303, lambda=0.013567
## - Fold09.Rep3: alpha=0.9303, lambda=0.013567
## + Fold09.Rep3: alpha=0.9076, lambda=3.206257
## - Fold09.Rep3: alpha=0.9076, lambda=3.206257
## + Fold09.Rep3: alpha=0.3536, lambda=3.736772
## - Fold09.Rep3: alpha=0.3536, lambda=3.736772
## + Fold09.Rep3: alpha=0.7569, lambda=0.457474
## - Fold09.Rep3: alpha=0.7569, lambda=0.457474
## + Fold09.Rep3: alpha=0.4423, lambda=0.004959
## - Fold09.Rep3: alpha=0.4423, lambda=0.004959
## + Fold09.Rep3: alpha=0.4111, lambda=0.885269
## - Fold09.Rep3: alpha=0.4111, lambda=0.885269
## + Fold09.Rep3: alpha=0.4419, lambda=0.014470
## - Fold09.Rep3: alpha=0.4419, lambda=0.014470
## + Fold09.Rep3: alpha=0.2539, lambda=6.506213
## - Fold09.Rep3: alpha=0.2539, lambda=6.506213
## + Fold10.Rep3: alpha=0.7034, lambda=0.215777
## - Fold10.Rep3: alpha=0.7034, lambda=0.215777
## + Fold10.Rep3: alpha=0.1303, lambda=2.918438
## - Fold10.Rep3: alpha=0.1303, lambda=2.918438
## + Fold10.Rep3: alpha=0.9303, lambda=0.013567
## - Fold10.Rep3: alpha=0.9303, lambda=0.013567
## + Fold10.Rep3: alpha=0.9076, lambda=3.206257
## - Fold10.Rep3: alpha=0.9076, lambda=3.206257
## + Fold10.Rep3: alpha=0.3536, lambda=3.736772
## - Fold10.Rep3: alpha=0.3536, lambda=3.736772
## + Fold10.Rep3: alpha=0.7569, lambda=0.457474
## - Fold10.Rep3: alpha=0.7569, lambda=0.457474
## + Fold10.Rep3: alpha=0.4423, lambda=0.004959
## - Fold10.Rep3: alpha=0.4423, lambda=0.004959
## + Fold10.Rep3: alpha=0.4111, lambda=0.885269
## - Fold10.Rep3: alpha=0.4111, lambda=0.885269
## + Fold10.Rep3: alpha=0.4419, lambda=0.014470
## - Fold10.Rep3: alpha=0.4419, lambda=0.014470
## + Fold10.Rep3: alpha=0.2539, lambda=6.506213
## - Fold10.Rep3: alpha=0.2539, lambda=6.506213
## + Fold01.Rep4: alpha=0.7034, lambda=0.215777
## - Fold01.Rep4: alpha=0.7034, lambda=0.215777
## + Fold01.Rep4: alpha=0.1303, lambda=2.918438
## - Fold01.Rep4: alpha=0.1303, lambda=2.918438
## + Fold01.Rep4: alpha=0.9303, lambda=0.013567
## - Fold01.Rep4: alpha=0.9303, lambda=0.013567
## + Fold01.Rep4: alpha=0.9076, lambda=3.206257
## - Fold01.Rep4: alpha=0.9076, lambda=3.206257
## + Fold01.Rep4: alpha=0.3536, lambda=3.736772
## - Fold01.Rep4: alpha=0.3536, lambda=3.736772
## + Fold01.Rep4: alpha=0.7569, lambda=0.457474
## - Fold01.Rep4: alpha=0.7569, lambda=0.457474
## + Fold01.Rep4: alpha=0.4423, lambda=0.004959
## - Fold01.Rep4: alpha=0.4423, lambda=0.004959
## + Fold01.Rep4: alpha=0.4111, lambda=0.885269
## - Fold01.Rep4: alpha=0.4111, lambda=0.885269
## + Fold01.Rep4: alpha=0.4419, lambda=0.014470
## - Fold01.Rep4: alpha=0.4419, lambda=0.014470
## + Fold01.Rep4: alpha=0.2539, lambda=6.506213
## - Fold01.Rep4: alpha=0.2539, lambda=6.506213
## + Fold02.Rep4: alpha=0.7034, lambda=0.215777
## - Fold02.Rep4: alpha=0.7034, lambda=0.215777
## + Fold02.Rep4: alpha=0.1303, lambda=2.918438
## - Fold02.Rep4: alpha=0.1303, lambda=2.918438
## + Fold02.Rep4: alpha=0.9303, lambda=0.013567
## - Fold02.Rep4: alpha=0.9303, lambda=0.013567
## + Fold02.Rep4: alpha=0.9076, lambda=3.206257
## - Fold02.Rep4: alpha=0.9076, lambda=3.206257
## + Fold02.Rep4: alpha=0.3536, lambda=3.736772
## - Fold02.Rep4: alpha=0.3536, lambda=3.736772
## + Fold02.Rep4: alpha=0.7569, lambda=0.457474
## - Fold02.Rep4: alpha=0.7569, lambda=0.457474
## + Fold02.Rep4: alpha=0.4423, lambda=0.004959
## - Fold02.Rep4: alpha=0.4423, lambda=0.004959
## + Fold02.Rep4: alpha=0.4111, lambda=0.885269
## - Fold02.Rep4: alpha=0.4111, lambda=0.885269
## + Fold02.Rep4: alpha=0.4419, lambda=0.014470
## - Fold02.Rep4: alpha=0.4419, lambda=0.014470
## + Fold02.Rep4: alpha=0.2539, lambda=6.506213
## - Fold02.Rep4: alpha=0.2539, lambda=6.506213
## + Fold03.Rep4: alpha=0.7034, lambda=0.215777
## - Fold03.Rep4: alpha=0.7034, lambda=0.215777
## + Fold03.Rep4: alpha=0.1303, lambda=2.918438
## - Fold03.Rep4: alpha=0.1303, lambda=2.918438
## + Fold03.Rep4: alpha=0.9303, lambda=0.013567
## - Fold03.Rep4: alpha=0.9303, lambda=0.013567
## + Fold03.Rep4: alpha=0.9076, lambda=3.206257
## - Fold03.Rep4: alpha=0.9076, lambda=3.206257
## + Fold03.Rep4: alpha=0.3536, lambda=3.736772
## - Fold03.Rep4: alpha=0.3536, lambda=3.736772
## + Fold03.Rep4: alpha=0.7569, lambda=0.457474
## - Fold03.Rep4: alpha=0.7569, lambda=0.457474
## + Fold03.Rep4: alpha=0.4423, lambda=0.004959
## - Fold03.Rep4: alpha=0.4423, lambda=0.004959
## + Fold03.Rep4: alpha=0.4111, lambda=0.885269
## - Fold03.Rep4: alpha=0.4111, lambda=0.885269
## + Fold03.Rep4: alpha=0.4419, lambda=0.014470
## - Fold03.Rep4: alpha=0.4419, lambda=0.014470
## + Fold03.Rep4: alpha=0.2539, lambda=6.506213
## - Fold03.Rep4: alpha=0.2539, lambda=6.506213
## + Fold04.Rep4: alpha=0.7034, lambda=0.215777
## - Fold04.Rep4: alpha=0.7034, lambda=0.215777
## + Fold04.Rep4: alpha=0.1303, lambda=2.918438
## - Fold04.Rep4: alpha=0.1303, lambda=2.918438
## + Fold04.Rep4: alpha=0.9303, lambda=0.013567
## - Fold04.Rep4: alpha=0.9303, lambda=0.013567
## + Fold04.Rep4: alpha=0.9076, lambda=3.206257
## - Fold04.Rep4: alpha=0.9076, lambda=3.206257
## + Fold04.Rep4: alpha=0.3536, lambda=3.736772
## - Fold04.Rep4: alpha=0.3536, lambda=3.736772
## + Fold04.Rep4: alpha=0.7569, lambda=0.457474
## - Fold04.Rep4: alpha=0.7569, lambda=0.457474
## + Fold04.Rep4: alpha=0.4423, lambda=0.004959
## - Fold04.Rep4: alpha=0.4423, lambda=0.004959
## + Fold04.Rep4: alpha=0.4111, lambda=0.885269
## - Fold04.Rep4: alpha=0.4111, lambda=0.885269
## + Fold04.Rep4: alpha=0.4419, lambda=0.014470
## - Fold04.Rep4: alpha=0.4419, lambda=0.014470
## + Fold04.Rep4: alpha=0.2539, lambda=6.506213
## - Fold04.Rep4: alpha=0.2539, lambda=6.506213
## + Fold05.Rep4: alpha=0.7034, lambda=0.215777
## - Fold05.Rep4: alpha=0.7034, lambda=0.215777
## + Fold05.Rep4: alpha=0.1303, lambda=2.918438
## - Fold05.Rep4: alpha=0.1303, lambda=2.918438
## + Fold05.Rep4: alpha=0.9303, lambda=0.013567
## - Fold05.Rep4: alpha=0.9303, lambda=0.013567
## + Fold05.Rep4: alpha=0.9076, lambda=3.206257
## - Fold05.Rep4: alpha=0.9076, lambda=3.206257
## + Fold05.Rep4: alpha=0.3536, lambda=3.736772
## - Fold05.Rep4: alpha=0.3536, lambda=3.736772
## + Fold05.Rep4: alpha=0.7569, lambda=0.457474
## - Fold05.Rep4: alpha=0.7569, lambda=0.457474
## + Fold05.Rep4: alpha=0.4423, lambda=0.004959
## - Fold05.Rep4: alpha=0.4423, lambda=0.004959
## + Fold05.Rep4: alpha=0.4111, lambda=0.885269
## - Fold05.Rep4: alpha=0.4111, lambda=0.885269
## + Fold05.Rep4: alpha=0.4419, lambda=0.014470
## - Fold05.Rep4: alpha=0.4419, lambda=0.014470
## + Fold05.Rep4: alpha=0.2539, lambda=6.506213
## - Fold05.Rep4: alpha=0.2539, lambda=6.506213
## + Fold06.Rep4: alpha=0.7034, lambda=0.215777
## - Fold06.Rep4: alpha=0.7034, lambda=0.215777
## + Fold06.Rep4: alpha=0.1303, lambda=2.918438
## - Fold06.Rep4: alpha=0.1303, lambda=2.918438
## + Fold06.Rep4: alpha=0.9303, lambda=0.013567
## - Fold06.Rep4: alpha=0.9303, lambda=0.013567
## + Fold06.Rep4: alpha=0.9076, lambda=3.206257
## - Fold06.Rep4: alpha=0.9076, lambda=3.206257
## + Fold06.Rep4: alpha=0.3536, lambda=3.736772
## - Fold06.Rep4: alpha=0.3536, lambda=3.736772
## + Fold06.Rep4: alpha=0.7569, lambda=0.457474
## - Fold06.Rep4: alpha=0.7569, lambda=0.457474
## + Fold06.Rep4: alpha=0.4423, lambda=0.004959
## - Fold06.Rep4: alpha=0.4423, lambda=0.004959
## + Fold06.Rep4: alpha=0.4111, lambda=0.885269
## - Fold06.Rep4: alpha=0.4111, lambda=0.885269
## + Fold06.Rep4: alpha=0.4419, lambda=0.014470
## - Fold06.Rep4: alpha=0.4419, lambda=0.014470
## + Fold06.Rep4: alpha=0.2539, lambda=6.506213
## - Fold06.Rep4: alpha=0.2539, lambda=6.506213
## + Fold07.Rep4: alpha=0.7034, lambda=0.215777
## - Fold07.Rep4: alpha=0.7034, lambda=0.215777
## + Fold07.Rep4: alpha=0.1303, lambda=2.918438
## - Fold07.Rep4: alpha=0.1303, lambda=2.918438
## + Fold07.Rep4: alpha=0.9303, lambda=0.013567
## - Fold07.Rep4: alpha=0.9303, lambda=0.013567
## + Fold07.Rep4: alpha=0.9076, lambda=3.206257
## - Fold07.Rep4: alpha=0.9076, lambda=3.206257
## + Fold07.Rep4: alpha=0.3536, lambda=3.736772
## - Fold07.Rep4: alpha=0.3536, lambda=3.736772
## + Fold07.Rep4: alpha=0.7569, lambda=0.457474
## - Fold07.Rep4: alpha=0.7569, lambda=0.457474
## + Fold07.Rep4: alpha=0.4423, lambda=0.004959
## - Fold07.Rep4: alpha=0.4423, lambda=0.004959
## + Fold07.Rep4: alpha=0.4111, lambda=0.885269
## - Fold07.Rep4: alpha=0.4111, lambda=0.885269
## + Fold07.Rep4: alpha=0.4419, lambda=0.014470
## - Fold07.Rep4: alpha=0.4419, lambda=0.014470
## + Fold07.Rep4: alpha=0.2539, lambda=6.506213
## - Fold07.Rep4: alpha=0.2539, lambda=6.506213
## + Fold08.Rep4: alpha=0.7034, lambda=0.215777
## - Fold08.Rep4: alpha=0.7034, lambda=0.215777
## + Fold08.Rep4: alpha=0.1303, lambda=2.918438
## - Fold08.Rep4: alpha=0.1303, lambda=2.918438
## + Fold08.Rep4: alpha=0.9303, lambda=0.013567
## - Fold08.Rep4: alpha=0.9303, lambda=0.013567
## + Fold08.Rep4: alpha=0.9076, lambda=3.206257
## - Fold08.Rep4: alpha=0.9076, lambda=3.206257
## + Fold08.Rep4: alpha=0.3536, lambda=3.736772
## - Fold08.Rep4: alpha=0.3536, lambda=3.736772
## + Fold08.Rep4: alpha=0.7569, lambda=0.457474
## - Fold08.Rep4: alpha=0.7569, lambda=0.457474
## + Fold08.Rep4: alpha=0.4423, lambda=0.004959
## - Fold08.Rep4: alpha=0.4423, lambda=0.004959
## + Fold08.Rep4: alpha=0.4111, lambda=0.885269
## - Fold08.Rep4: alpha=0.4111, lambda=0.885269
## + Fold08.Rep4: alpha=0.4419, lambda=0.014470
## - Fold08.Rep4: alpha=0.4419, lambda=0.014470
## + Fold08.Rep4: alpha=0.2539, lambda=6.506213
## - Fold08.Rep4: alpha=0.2539, lambda=6.506213
## + Fold09.Rep4: alpha=0.7034, lambda=0.215777
## - Fold09.Rep4: alpha=0.7034, lambda=0.215777
## + Fold09.Rep4: alpha=0.1303, lambda=2.918438
## - Fold09.Rep4: alpha=0.1303, lambda=2.918438
## + Fold09.Rep4: alpha=0.9303, lambda=0.013567
## - Fold09.Rep4: alpha=0.9303, lambda=0.013567
## + Fold09.Rep4: alpha=0.9076, lambda=3.206257
## - Fold09.Rep4: alpha=0.9076, lambda=3.206257
## + Fold09.Rep4: alpha=0.3536, lambda=3.736772
## - Fold09.Rep4: alpha=0.3536, lambda=3.736772
## + Fold09.Rep4: alpha=0.7569, lambda=0.457474
## - Fold09.Rep4: alpha=0.7569, lambda=0.457474
## + Fold09.Rep4: alpha=0.4423, lambda=0.004959
## - Fold09.Rep4: alpha=0.4423, lambda=0.004959
## + Fold09.Rep4: alpha=0.4111, lambda=0.885269
## - Fold09.Rep4: alpha=0.4111, lambda=0.885269
## + Fold09.Rep4: alpha=0.4419, lambda=0.014470
## - Fold09.Rep4: alpha=0.4419, lambda=0.014470
## + Fold09.Rep4: alpha=0.2539, lambda=6.506213
## - Fold09.Rep4: alpha=0.2539, lambda=6.506213
## + Fold10.Rep4: alpha=0.7034, lambda=0.215777
## - Fold10.Rep4: alpha=0.7034, lambda=0.215777
## + Fold10.Rep4: alpha=0.1303, lambda=2.918438
## - Fold10.Rep4: alpha=0.1303, lambda=2.918438
## + Fold10.Rep4: alpha=0.9303, lambda=0.013567
## - Fold10.Rep4: alpha=0.9303, lambda=0.013567
## + Fold10.Rep4: alpha=0.9076, lambda=3.206257
## - Fold10.Rep4: alpha=0.9076, lambda=3.206257
## + Fold10.Rep4: alpha=0.3536, lambda=3.736772
## - Fold10.Rep4: alpha=0.3536, lambda=3.736772
## + Fold10.Rep4: alpha=0.7569, lambda=0.457474
## - Fold10.Rep4: alpha=0.7569, lambda=0.457474
## + Fold10.Rep4: alpha=0.4423, lambda=0.004959
## - Fold10.Rep4: alpha=0.4423, lambda=0.004959
## + Fold10.Rep4: alpha=0.4111, lambda=0.885269
## - Fold10.Rep4: alpha=0.4111, lambda=0.885269
## + Fold10.Rep4: alpha=0.4419, lambda=0.014470
## - Fold10.Rep4: alpha=0.4419, lambda=0.014470
## + Fold10.Rep4: alpha=0.2539, lambda=6.506213
## - Fold10.Rep4: alpha=0.2539, lambda=6.506213
## + Fold01.Rep5: alpha=0.7034, lambda=0.215777
## - Fold01.Rep5: alpha=0.7034, lambda=0.215777
## + Fold01.Rep5: alpha=0.1303, lambda=2.918438
## - Fold01.Rep5: alpha=0.1303, lambda=2.918438
## + Fold01.Rep5: alpha=0.9303, lambda=0.013567
## - Fold01.Rep5: alpha=0.9303, lambda=0.013567
## + Fold01.Rep5: alpha=0.9076, lambda=3.206257
## - Fold01.Rep5: alpha=0.9076, lambda=3.206257
## + Fold01.Rep5: alpha=0.3536, lambda=3.736772
## - Fold01.Rep5: alpha=0.3536, lambda=3.736772
## + Fold01.Rep5: alpha=0.7569, lambda=0.457474
## - Fold01.Rep5: alpha=0.7569, lambda=0.457474
## + Fold01.Rep5: alpha=0.4423, lambda=0.004959
## - Fold01.Rep5: alpha=0.4423, lambda=0.004959
## + Fold01.Rep5: alpha=0.4111, lambda=0.885269
## - Fold01.Rep5: alpha=0.4111, lambda=0.885269
## + Fold01.Rep5: alpha=0.4419, lambda=0.014470
## - Fold01.Rep5: alpha=0.4419, lambda=0.014470
## + Fold01.Rep5: alpha=0.2539, lambda=6.506213
## - Fold01.Rep5: alpha=0.2539, lambda=6.506213
## + Fold02.Rep5: alpha=0.7034, lambda=0.215777
## - Fold02.Rep5: alpha=0.7034, lambda=0.215777
## + Fold02.Rep5: alpha=0.1303, lambda=2.918438
## - Fold02.Rep5: alpha=0.1303, lambda=2.918438
## + Fold02.Rep5: alpha=0.9303, lambda=0.013567
## - Fold02.Rep5: alpha=0.9303, lambda=0.013567
## + Fold02.Rep5: alpha=0.9076, lambda=3.206257
## - Fold02.Rep5: alpha=0.9076, lambda=3.206257
## + Fold02.Rep5: alpha=0.3536, lambda=3.736772
## - Fold02.Rep5: alpha=0.3536, lambda=3.736772
## + Fold02.Rep5: alpha=0.7569, lambda=0.457474
## - Fold02.Rep5: alpha=0.7569, lambda=0.457474
## + Fold02.Rep5: alpha=0.4423, lambda=0.004959
## - Fold02.Rep5: alpha=0.4423, lambda=0.004959
## + Fold02.Rep5: alpha=0.4111, lambda=0.885269
## - Fold02.Rep5: alpha=0.4111, lambda=0.885269
## + Fold02.Rep5: alpha=0.4419, lambda=0.014470
## - Fold02.Rep5: alpha=0.4419, lambda=0.014470
## + Fold02.Rep5: alpha=0.2539, lambda=6.506213
## - Fold02.Rep5: alpha=0.2539, lambda=6.506213
## + Fold03.Rep5: alpha=0.7034, lambda=0.215777
## - Fold03.Rep5: alpha=0.7034, lambda=0.215777
## + Fold03.Rep5: alpha=0.1303, lambda=2.918438
## - Fold03.Rep5: alpha=0.1303, lambda=2.918438
## + Fold03.Rep5: alpha=0.9303, lambda=0.013567
## - Fold03.Rep5: alpha=0.9303, lambda=0.013567
## + Fold03.Rep5: alpha=0.9076, lambda=3.206257
## - Fold03.Rep5: alpha=0.9076, lambda=3.206257
## + Fold03.Rep5: alpha=0.3536, lambda=3.736772
## - Fold03.Rep5: alpha=0.3536, lambda=3.736772
## + Fold03.Rep5: alpha=0.7569, lambda=0.457474
## - Fold03.Rep5: alpha=0.7569, lambda=0.457474
## + Fold03.Rep5: alpha=0.4423, lambda=0.004959
## - Fold03.Rep5: alpha=0.4423, lambda=0.004959
## + Fold03.Rep5: alpha=0.4111, lambda=0.885269
## - Fold03.Rep5: alpha=0.4111, lambda=0.885269
## + Fold03.Rep5: alpha=0.4419, lambda=0.014470
## - Fold03.Rep5: alpha=0.4419, lambda=0.014470
## + Fold03.Rep5: alpha=0.2539, lambda=6.506213
## - Fold03.Rep5: alpha=0.2539, lambda=6.506213
## + Fold04.Rep5: alpha=0.7034, lambda=0.215777
## - Fold04.Rep5: alpha=0.7034, lambda=0.215777
## + Fold04.Rep5: alpha=0.1303, lambda=2.918438
## - Fold04.Rep5: alpha=0.1303, lambda=2.918438
## + Fold04.Rep5: alpha=0.9303, lambda=0.013567
## - Fold04.Rep5: alpha=0.9303, lambda=0.013567
## + Fold04.Rep5: alpha=0.9076, lambda=3.206257
## - Fold04.Rep5: alpha=0.9076, lambda=3.206257
## + Fold04.Rep5: alpha=0.3536, lambda=3.736772
## - Fold04.Rep5: alpha=0.3536, lambda=3.736772
## + Fold04.Rep5: alpha=0.7569, lambda=0.457474
## - Fold04.Rep5: alpha=0.7569, lambda=0.457474
## + Fold04.Rep5: alpha=0.4423, lambda=0.004959
## - Fold04.Rep5: alpha=0.4423, lambda=0.004959
## + Fold04.Rep5: alpha=0.4111, lambda=0.885269
## - Fold04.Rep5: alpha=0.4111, lambda=0.885269
## + Fold04.Rep5: alpha=0.4419, lambda=0.014470
## - Fold04.Rep5: alpha=0.4419, lambda=0.014470
## + Fold04.Rep5: alpha=0.2539, lambda=6.506213
## - Fold04.Rep5: alpha=0.2539, lambda=6.506213
## + Fold05.Rep5: alpha=0.7034, lambda=0.215777
## - Fold05.Rep5: alpha=0.7034, lambda=0.215777
## + Fold05.Rep5: alpha=0.1303, lambda=2.918438
## - Fold05.Rep5: alpha=0.1303, lambda=2.918438
## + Fold05.Rep5: alpha=0.9303, lambda=0.013567
## - Fold05.Rep5: alpha=0.9303, lambda=0.013567
## + Fold05.Rep5: alpha=0.9076, lambda=3.206257
## - Fold05.Rep5: alpha=0.9076, lambda=3.206257
## + Fold05.Rep5: alpha=0.3536, lambda=3.736772
## - Fold05.Rep5: alpha=0.3536, lambda=3.736772
## + Fold05.Rep5: alpha=0.7569, lambda=0.457474
## - Fold05.Rep5: alpha=0.7569, lambda=0.457474
## + Fold05.Rep5: alpha=0.4423, lambda=0.004959
## - Fold05.Rep5: alpha=0.4423, lambda=0.004959
## + Fold05.Rep5: alpha=0.4111, lambda=0.885269
## - Fold05.Rep5: alpha=0.4111, lambda=0.885269
## + Fold05.Rep5: alpha=0.4419, lambda=0.014470
## - Fold05.Rep5: alpha=0.4419, lambda=0.014470
## + Fold05.Rep5: alpha=0.2539, lambda=6.506213
## - Fold05.Rep5: alpha=0.2539, lambda=6.506213
## + Fold06.Rep5: alpha=0.7034, lambda=0.215777
## - Fold06.Rep5: alpha=0.7034, lambda=0.215777
## + Fold06.Rep5: alpha=0.1303, lambda=2.918438
## - Fold06.Rep5: alpha=0.1303, lambda=2.918438
## + Fold06.Rep5: alpha=0.9303, lambda=0.013567
## - Fold06.Rep5: alpha=0.9303, lambda=0.013567
## + Fold06.Rep5: alpha=0.9076, lambda=3.206257
## - Fold06.Rep5: alpha=0.9076, lambda=3.206257
## + Fold06.Rep5: alpha=0.3536, lambda=3.736772
## - Fold06.Rep5: alpha=0.3536, lambda=3.736772
## + Fold06.Rep5: alpha=0.7569, lambda=0.457474
## - Fold06.Rep5: alpha=0.7569, lambda=0.457474
## + Fold06.Rep5: alpha=0.4423, lambda=0.004959
## - Fold06.Rep5: alpha=0.4423, lambda=0.004959
## + Fold06.Rep5: alpha=0.4111, lambda=0.885269
## - Fold06.Rep5: alpha=0.4111, lambda=0.885269
## + Fold06.Rep5: alpha=0.4419, lambda=0.014470
## - Fold06.Rep5: alpha=0.4419, lambda=0.014470
## + Fold06.Rep5: alpha=0.2539, lambda=6.506213
## - Fold06.Rep5: alpha=0.2539, lambda=6.506213
## + Fold07.Rep5: alpha=0.7034, lambda=0.215777
## - Fold07.Rep5: alpha=0.7034, lambda=0.215777
## + Fold07.Rep5: alpha=0.1303, lambda=2.918438
## - Fold07.Rep5: alpha=0.1303, lambda=2.918438
## + Fold07.Rep5: alpha=0.9303, lambda=0.013567
## - Fold07.Rep5: alpha=0.9303, lambda=0.013567
## + Fold07.Rep5: alpha=0.9076, lambda=3.206257
## - Fold07.Rep5: alpha=0.9076, lambda=3.206257
## + Fold07.Rep5: alpha=0.3536, lambda=3.736772
## - Fold07.Rep5: alpha=0.3536, lambda=3.736772
## + Fold07.Rep5: alpha=0.7569, lambda=0.457474
## - Fold07.Rep5: alpha=0.7569, lambda=0.457474
## + Fold07.Rep5: alpha=0.4423, lambda=0.004959
## - Fold07.Rep5: alpha=0.4423, lambda=0.004959
## + Fold07.Rep5: alpha=0.4111, lambda=0.885269
## - Fold07.Rep5: alpha=0.4111, lambda=0.885269
## + Fold07.Rep5: alpha=0.4419, lambda=0.014470
## - Fold07.Rep5: alpha=0.4419, lambda=0.014470
## + Fold07.Rep5: alpha=0.2539, lambda=6.506213
## - Fold07.Rep5: alpha=0.2539, lambda=6.506213
## + Fold08.Rep5: alpha=0.7034, lambda=0.215777
## - Fold08.Rep5: alpha=0.7034, lambda=0.215777
## + Fold08.Rep5: alpha=0.1303, lambda=2.918438
## - Fold08.Rep5: alpha=0.1303, lambda=2.918438
## + Fold08.Rep5: alpha=0.9303, lambda=0.013567
## - Fold08.Rep5: alpha=0.9303, lambda=0.013567
## + Fold08.Rep5: alpha=0.9076, lambda=3.206257
## - Fold08.Rep5: alpha=0.9076, lambda=3.206257
## + Fold08.Rep5: alpha=0.3536, lambda=3.736772
## - Fold08.Rep5: alpha=0.3536, lambda=3.736772
## + Fold08.Rep5: alpha=0.7569, lambda=0.457474
## - Fold08.Rep5: alpha=0.7569, lambda=0.457474
## + Fold08.Rep5: alpha=0.4423, lambda=0.004959
## - Fold08.Rep5: alpha=0.4423, lambda=0.004959
## + Fold08.Rep5: alpha=0.4111, lambda=0.885269
## - Fold08.Rep5: alpha=0.4111, lambda=0.885269
## + Fold08.Rep5: alpha=0.4419, lambda=0.014470
## - Fold08.Rep5: alpha=0.4419, lambda=0.014470
## + Fold08.Rep5: alpha=0.2539, lambda=6.506213
## - Fold08.Rep5: alpha=0.2539, lambda=6.506213
## + Fold09.Rep5: alpha=0.7034, lambda=0.215777
## - Fold09.Rep5: alpha=0.7034, lambda=0.215777
## + Fold09.Rep5: alpha=0.1303, lambda=2.918438
## - Fold09.Rep5: alpha=0.1303, lambda=2.918438
## + Fold09.Rep5: alpha=0.9303, lambda=0.013567
## - Fold09.Rep5: alpha=0.9303, lambda=0.013567
## + Fold09.Rep5: alpha=0.9076, lambda=3.206257
## - Fold09.Rep5: alpha=0.9076, lambda=3.206257
## + Fold09.Rep5: alpha=0.3536, lambda=3.736772
## - Fold09.Rep5: alpha=0.3536, lambda=3.736772
## + Fold09.Rep5: alpha=0.7569, lambda=0.457474
## - Fold09.Rep5: alpha=0.7569, lambda=0.457474
## + Fold09.Rep5: alpha=0.4423, lambda=0.004959
## - Fold09.Rep5: alpha=0.4423, lambda=0.004959
## + Fold09.Rep5: alpha=0.4111, lambda=0.885269
## - Fold09.Rep5: alpha=0.4111, lambda=0.885269
## + Fold09.Rep5: alpha=0.4419, lambda=0.014470
## - Fold09.Rep5: alpha=0.4419, lambda=0.014470
## + Fold09.Rep5: alpha=0.2539, lambda=6.506213
## - Fold09.Rep5: alpha=0.2539, lambda=6.506213
## + Fold10.Rep5: alpha=0.7034, lambda=0.215777
## - Fold10.Rep5: alpha=0.7034, lambda=0.215777
## + Fold10.Rep5: alpha=0.1303, lambda=2.918438
## - Fold10.Rep5: alpha=0.1303, lambda=2.918438
## + Fold10.Rep5: alpha=0.9303, lambda=0.013567
## - Fold10.Rep5: alpha=0.9303, lambda=0.013567
## + Fold10.Rep5: alpha=0.9076, lambda=3.206257
## - Fold10.Rep5: alpha=0.9076, lambda=3.206257
## + Fold10.Rep5: alpha=0.3536, lambda=3.736772
## - Fold10.Rep5: alpha=0.3536, lambda=3.736772
## + Fold10.Rep5: alpha=0.7569, lambda=0.457474
## - Fold10.Rep5: alpha=0.7569, lambda=0.457474
## + Fold10.Rep5: alpha=0.4423, lambda=0.004959
## - Fold10.Rep5: alpha=0.4423, lambda=0.004959
## + Fold10.Rep5: alpha=0.4111, lambda=0.885269
## - Fold10.Rep5: alpha=0.4111, lambda=0.885269
## + Fold10.Rep5: alpha=0.4419, lambda=0.014470
## - Fold10.Rep5: alpha=0.4419, lambda=0.014470
## + Fold10.Rep5: alpha=0.2539, lambda=6.506213
## - Fold10.Rep5: alpha=0.2539, lambda=6.506213
## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo, :
## There were missing values in resampled performance measures.
## Aggregating results
## Selecting tuning parameters
## Fitting alpha = 0.442, lambda = 0.00496 on full training set
# Best tuning parameter
elastic_reg$bestTune
## alpha lambda
## 6 0.4422599 0.004958862
# Make predictions on training set
predictions_train <- predict(elastic_reg, x)
eval_results(y_train, predictions_train, train)
## RMSE Rsquare
## 1 0.6438077 0.3457911
# Make predictions on test set
predictions_test <- predict(elastic_reg, x_test)
eval_results(y_test, predictions_test, test)
## RMSE Rsquare
## 1 0.6547278 0.3824665